Non-Abelian Brill-Noether theory and Fano 3-folds

TL;DR

This paper explores the structure of Brill-Noether loci in the context of non-Abelian bundles, revealing new geometric insights and applications to Fano 3-folds and other algebraic varieties.

Contribution

It introduces novel determinantal methods for analyzing non-Abelian Brill-Noether loci, extending classical theories to new geometric settings.

Findings

New determinantal descriptions of Brill-Noether loci

Applications to Fano 3-folds and K3 surfaces

Enhanced understanding of moduli of vector bundles

Abstract

A Brill-Noether locus is a subscheme of the moduli of bundles E over a curve C defined by requiring E to have a given number of sections, or homomorphisms from another bundle. There are a number of different types, that can be treated by determinantal methods, with symmetry or skewsymmetry arising from Serre duality. They have many beautiful applications to curves, K3 surfaces and Fano 3-folds.